Given the demand function Q_X = 5,000 - 250P_X +120P_Y +.04I where P_Y= $50.00 and I = $60,000, marginal revenue will be zero where Q = 6700.

Question

Quizplus · Accepted Answer

To find the point where marginal revenue (MR) is zero, we need to take the derivative of the demand function with respect to quantity (Q) and set it equal to zero. Solving for Q gives us the quantity where MR is zero. Taking the derivative: d(Q_X)/dQ = -250 + 120P_Y Setting equal to zero and plugging in the given values: -250 + 120(50) = 0 Solving for Q: 5000 - 250Q + 120(50) + 0.04(60000) = 6700P 5000 - 250Q + 6000 + 2400 = 6700P P = (11000 - 250Q)/6700 MR = 6700(1 - Q_X/5000 - 1.2P_Y/5000 - 0.04I/5000) Setting MR equal to zero and plugging in Q = 6700: 0 = 6700(1 - 6700/5000 - 1.2(50)/5000 - 0.04(60000)/5000) Simplifying, we get MR = $0 exactly where Q = 6700. Therefore, the statement is true.

Given the Demand Function QX = 5,000 - 250PX +120PY

Given the Demand Function Q_X = 5,000 - 250P_X +120P_Y